An analytical model of an elementary elliptical cell forming an alveolar elastic material under plane stress

This paper analyzes the static behavior of alveoled materials that is about to be developed for dynamic optimization of structural panels. It deals precisely with materials made of elliptical thin cells, filled with polymer material. The main contribution of the paperconsists in elaborating an analytical approach describing the material. The considered problem represents an unidirectional stress, the goal being to calculate the elastic energy and strain globally obtained in the material. The wall of the elementary cell is represented in accordance with the classical BRESSE's theory of thin beams, with specific adaptation for elliptical shape. The polymer material filling the cell is modelized with ABSI!s method of equivalence, which allows a direct approximation of various continuous media by equivalent spring segments. This method is presented and discussed for the present configuration, with its specific adaptation. The final result obtained by these analytical approaches is then compared to results from a finite element model. In spite of local differences between the analytical results and numerical computation, it appears clearly that the precision obtained by the proposed analytical approach is better than 95%, which is sufficient for this kind of material. Thus, the proposed analytical calculation and methodology allows robust and quick determination of material characteristics for elementary cells of such alveoled materials. The resulting laws can then be introduced into global models of a grid of cells

On free conformal and vertex algebras

Any variety of classical algebras has a so-called conformal counterpart. For example one can consider Lie conformal or associative conformal algebras. Lie conformal algebras are closely related to vertex algebras. We define free objects in the categories of conformal and vertex algebras. In some cases we can explicitly build their Groebner bases.Comment: AMS-LaTeX, 19 pages. To process, run "latex freecv.tex

Two-photon imaging through a multimode fiber

In this work we demonstrate 3D imaging using two-photon excitation through a 20 cm long multimode optical fiber (MMF) of 350 micrometers diameter. The imaging principle is similar to single photon fluorescence through a MMF, except that a focused femtosecond pulse is delivered and scanned over the sample. In our approach, focusing and scanning through the fiber is accomplished by digital phase conjugation using mode selection by time gating with an ultra-fast reference pulse. The excited two-photon emission is collected through the same fiber. We demonstrate depth sectioning by scanning the focused pulse in a 3D volume over a sample consisting of fluorescent beads suspended in a polymer. The achieved resolution is 1 micrometer laterally and 15 micrometers axially. Scanning is performed over an 80x80 micrometers field of view. To our knowledge, this is the first demonstration of high-resolution three-dimensional imaging using two-photon fluorescence through a multimode fiber